Lots of day hikes directly behind Santa Barbara in the front country mountains. Most follow the creeks up the canyons and eventually top out on the top of the ridge line (Camino Cielo). These are all just day hikes.

If you're looking for a longer overnight hike, head over the hill into the Santa Ynez valley to access the SB backcountry and adjacent wilderness areas (San Rafael and Dick Smith Wildernesses).

Ojai area (just south and inland of SB) also has lots of good hikes and access to the Sespe Wilderness.

I do most of my hiking in the local SB and Ojai backcountry. The santabarbarahikes.com website is a good resource as are the hiking maps made by Bryan Conant, which are available at any of the local hiking shops.